17 found
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Amílcar Sernadas [11]A. Sernadas [9]Amlcar Sernadas [1]
  1. Fibring: Completeness Preservation.Alberto Zanardo, Amilcar Sernadas & Cristina Sernadas - 2001 - Journal of Symbolic Logic 66 (1):414-439.
    A completeness theorem is established for logics with congruence endowed with general semantics (in the style of general frames). As a corollary, completeness is shown to be preserved by fibring logics with congruence provided that congruence is retained in the resulting logic. The class of logics with equivalence is shown to be closed under fibring and to be included in the class of logics with congruence. Thus, completeness is shown to be preserved by fibring logics with equivalence and general semantics. (...)
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  2.  39
    Fibring Non-Truth-Functional Logics: Completeness Preservation.C. Caleiro, W. A. Carnielli, M. E. Coniglio, A. Sernadas & C. Sernadas - 2003 - Journal of Logic, Language and Information 12 (2):183-211.
    Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can still be dealt with. Furthermore, it is shown that thisextended notion of fibring preserves completeness under certain reasonableconditions. This completeness transfer (...)
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  3.  8
    A Graph-Theoretic Account of Logics.A. Sernadas, C. Sernadas, J. Rasga & Marcelo E. Coniglio - 2009 - Journal of Logic and Computation 19 (6):1281-1320.
    A graph-theoretic account of logics is explored based on the general notion of m-graph (that is, a graph where each edge can have a finite sequence of nodes as source). Signatures, interpretation structures and deduction systems are seen as m-graphs. After defining a category freely generated by a m-graph, formulas and expressions in general can be seen as morphisms. Moreover, derivations involving rule instantiation are also morphisms. Soundness and completeness theorems are proved. As a consequence of the generality of the (...)
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  4.  7
    Importing Logics.João Rasga, Amílcar Sernadas & Cristina Sernadas - 2012 - Studia Logica 100 (3):545-581.
    The novel notion of importing logics is introduced, subsuming as special cases several kinds of asymmetric combination mechanisms, like temporalization [8, 9], modalization [7] and exogenous enrichment [13, 5, 12, 4, 1]. The graph-theoretic approach proposed in [15] is used, but formulas are identified with irreducible paths in the signature multi-graph instead of equivalence classes of such paths, facilitating proofs involving inductions on formulas. Importing is proved to be strongly conservative. Conservative results follow as corollaries for temporalization, modalization and exogenous (...)
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  5.  12
    Craig Interpolation in the Presence of Unreliable Connectives.João Rasga, Cristina Sernadas & Amlcar Sernadas - 2014 - Logica Universalis 8 (3-4):423-446.
    Arrow and turnstile interpolations are investigated in UCL [introduced by Sernadas et al. ], a logic that is a complete extension of classical propositional logic for reasoning about connectives that only behave as expected with a given probability. Arrow interpolation is shown to hold in general and turnstile interpolation is established under some provisos.
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  6.  12
    Importing Logics: Soundness and Completeness Preservation. [REVIEW]J. Rasga, A. Sernadas & C. Sernadas - 2013 - Studia Logica 101 (1):117-155.
    Importing subsumes several asymmetric ways of combining logics, including modalization and temporalization. A calculus is provided for importing, inheriting the axioms and rules from the given logics and including additional rules for lifting derivations from the imported logic. The calculus is shown to be sound and concretely complete with respect to the semantics of importing as proposed in J. Rasga et al. (100(3):541–581, 2012) Studia Logica.
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  7.  5
    Decision and Optimization Problems in the Unreliable-Circuit Logic.J. Rasga, C. Sernadas, P. Mateus & A. Sernadas - 2017 - Logic Journal of the IGPL 25 (3):283-308.
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  8.  20
    Synchronization of Logics.Amílcar Sernadas, Cristina Sernadas & Carlos Caleiro - 1997 - Studia Logica 59 (2):217-247.
    Motivated by applications in software engineering, we propose two forms of combination of logics: synchronization on formulae and synchronization on models. We start by reviewing satisfaction systems, consequence systems, one-step derivation systems and theory spaces, as well as their functorial relationships. We define the synchronization on formulae of two consequence systems and provide a categorial characterization of the construction. For illustration we consider the synchronization of linear temporal logic and equational logic. We define the synchronization on models of two satisfaction (...)
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  9.  2
    Fibring: Completeness Preservation.Alberto Zanardo, Amilcar Sernadas & Cristina Sernadas - 2001 - Journal of Symbolic Logic 66 (1):414-439.
    A completeness theorem is established for logics with congruence endowed with general semantics. As a corollary, completeness is shown to be preserved by fibring logics with congruence provided that congruence is retained in the resulting logic. The class of logics with equivalence is shown to be closed under fibring and to be included in the class of logics with congruence. Thus, completeness is shown to be preserved by fibring logics with equivalence and general semantics. An example is provided showing that (...)
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  10.  20
    On Graph-Theoretic Fibring of Logics.A. Sernadas, C. Sernadas, J. Rasga & M. Coniglio - 2009 - Journal of Logic and Computation 19 (6):1321-1357.
    A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as a multi-graph (m-graph) where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is a multi-graph (m-graph) where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of two deductive systems is an (...)
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  11.  19
    Fibring Logics, Dov M. Gabbay.Amílcar Sernadas - 2000 - Journal of Logic, Language and Information 9 (4):511-513.
  12.  9
    On Combined Connectives.A. Sernadas, C. Sernadas & J. Rasga - 2011 - Logica Universalis 5 (2):205-224.
    Combined connectives arise in combined logics. In fibrings, such combined connectives are known as shared connectives and inherit the logical properties of each component. A new way of combining connectives (and other language constructors of propositional nature) is proposed by inheriting only the common logical properties of the components. A sound and complete calculus is provided for reasoning about the latter. The calculus is shown to be a conservative extension of the original calculus. Examples are provided contributing to a better (...)
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  13.  6
    Fibring Modal First-Order Logics: Completeness Preservation.Amilcar Sernadas, Cristina Sernadas & Alberto Zanardo - 2002 - Logic Journal of the IGPL 10 (4):413-451.
    Fibring is defined as a mechanism for combining logics with a first-order base, at both the semantic and deductive levels. A completeness theorem is established for a wide class of such logics, using a variation of the Henkin method that takes advantage of the presence of equality and inequality in the logic. As a corollary, completeness is shown to be preserved when fibring logics in that class. A modal first-order logic is obtained as a fibring where neither the Barcan formula (...)
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  14.  6
    Fibring as Biporting Subsumes Asymmetric Combinations.J. Rasga, A. Sernadas & C. Sernadas - 2014 - Studia Logica 102 (5):1041-1074.
    The transference of preservation results between importing and unconstrained fibring is investigated. For that purpose, a new formulation of fibring, called biporting, is introduced, and importing is shown to be subsumed by biporting. In consequence, particular cases of importing, like temporalization, modalization and globalization are subsumed by fibring. Capitalizing on these results, the preservation of the finite model property by fibring is transferred to importing and then carried over to globalization.
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  15.  5
    Truth-Values as Labels: A General Recipe for Labelled Deduction.Cristina Sernadas, Luca Viganò, João Rasga & Amílcar Sernadas - 2003 - Journal of Applied Non-Classical Logics 13 (3-4):277-315.
  16. Dov M. Gabbay, Fibring Logics.A. Sernadas - 2000 - Journal of Logic Language and Information 9 (4):511-513.
  17.  1
    Preservation of Craig Interpolation by the Product of Matrix Logics.C. Sernadas, J. Rasga & A. Sernadas - 2013 - Journal of Applied Logic 11 (3):328-349.